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On free semilattice-ordered semigroups satisfying x n=x

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Abstract

Let B(k,0,n) denote the group with k generators which is free in the group variety defined by the identity x n=1. Let B slo (k,1,n) denote the semilattice-ordered semigroup with k generators which is free in the semilattice-ordered semigroup variety defined by the identity x n=x. We prove a generalization of the Green-Rees theorem: B slo (k,1,n) is finite for all k≥1 if and only if B(k,0,n−1) is finite for all k≥1. We find a formula for card(B slo (1,1,n)). We construct B slo (k,1,n) for some concrete values of k and n.

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  1. Katedra matematiky PrF UJEP, Ceske mladeze 8, 400 96, Usti nad Labem, Czech Republic

    Petr Gajdoš & Martin Kuřil

Authors
  1. Petr Gajdoš
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  2. Martin Kuřil
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Correspondence to Martin Kuřil.

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Communicated by Francis J. Pastijn.

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Gajdoš, P., Kuřil, M. On free semilattice-ordered semigroups satisfying x n=x . Semigroup Forum 80, 92–104 (2010). https://doi.org/10.1007/s00233-009-9188-3

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  • DOI: https://doi.org/10.1007/s00233-009-9188-3

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